I'm a Christian but I have never believed that non - religious people are horrible with no morals. I've always said that I care more about a person's morality over religion. Morality and religion are NOT synonymous.
To most Christians the bible is like a software license. Nobody actually reads it. They just scroll to the bottom and click I agree. Many of us who search for meaning, read the Christian Bible more closely than the Tea Party types ever will.
The fact that you can have an absolute like "true morality" requires that there be a standard of morality. How is there a standard if there is no God? If a supreme being is not in the picture, there can be no morality at all.